Solve for $x$ and $y$ using elimination. ${2x+2y = 32}$ ${-3x-6y = -69}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ ${6x+6y = 96}$ $-3x-6y = -69$ Add the top and bottom equations together. $3x = 27$ $\dfrac{3x}{{3}} = \dfrac{27}{{3}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {2x+2y = 32}\thinspace$ to find $y$ ${2}{(9)}{ + 2y = 32}$ $18+2y = 32$ $18{-18} + 2y = 32{-18}$ $2y = 14$ $\dfrac{2y}{{2}} = \dfrac{14}{{2}}$ ${y = 7}$ You can also plug ${x = 9}$ into $\thinspace {-3x-6y = -69}\thinspace$ and get the same answer for $y$ : ${-3}{(9)}{ - 6y = -69}$ ${y = 7}$